03110nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183072001500206100007900221245015500300250001800455264006900473300006400542336002600606337002600632338003600658347002400694505022500718520126500943650002902208650002402237650001402261650002402275650001902299650002902318650002702347650003102374650002102405710003402426773002602460776003602486776003602522776003602558856004602594978-3-031-48472-8DE-He21320251030113252.0cr nn 008mamaa241031s2024    sz |    s    |||| 0|eng d  a97830314847287 a10.1007/978-3-031-48472-82doi 4aTA329-348 7aTBJ2bicssc 7aMAT0030002bisacsh 7aTBJ2thema1 aLuo, Albert C. J.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aTwo-dimensional Single-Variable Cubic Nonlinear Systems, Vol. Ih[electronic resource] :bA Self-univariate Cubic Vector Field /cby Albert C. J. Luo.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aIX, 437 p. 32 illus., 31 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aChapter 1 Constant and Self-cubic Vector fields -- Chapter 2 Crossing-linear and Self-cubic Vector Fields -- Chapter 3 Crossing-quadratic and Self-Cubic Vector Fields -- Chapter 4 Two Single-variable Cubic Vector Fields.  aThis book, the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows. Develops the theory for 1-dimensonal flow singularity and bifurcations to elucidate dynamics of nonlinear systems; Provides a new research direction in nonlinear dynamics community; Shows how singularity and bifurcations occur not only for equilibriums and attractors but also for 1-dimensional flows. 0aEngineering mathematics. 0aMechanics, Applied. 0aDynamics. 0aNonlinear theories. 0aSystem theory.14aEngineering Mathematics.24aEngineering Mechanics.24aApplied Dynamical Systems.24aComplex Systems.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303148471108iPrinted edition:z978303148473508iPrinted edition:z978303148474240uhttps://doi.org/10.1007/978-3-031-48472-8